Build-up of internal cake in layered filtering media

The goal of improving the design of a filtering medium often leads to a layered construction. The intention is to distribute a polydisperse dust more evenly over the whole depth of the medium. However, due to the different properties of the multiple layers, it can happen that some of the particles cannot pass one of the layers any more. Thus, an internal cake is likely to grow at the interface between two layers of a layered medium. In this study, a macroscopic model for the build-up of an internal cake is derived. The approach is based on a model for external cake filtration. Besides the well-known equations for depth filtration, a more detailed treatment of the flux over the interface is necessary to describe the growth of the internal cake. Therefore, interface conditions and an evolution equation to describe the movement of the internal cake surface are derived. In contrast to an external filter cake, the internal cake is mostly consisting of small and medium-sized particles since the large particles are already deposited in the first layer of the filtering medium. The internal cake starts to grow as soon as a critical porosity is reached in the clogging layer. From this point on, the newly derived interface conditions become important. For the computation of the pressure drop, a hybrid model with three contributions is used, namely the contribution from the clean medium, depth and internal cake filtration. For the latter two parts, a modified Kozeny-Carman model based on average diameters is used. A filtering medium consisting of two layers, a prefilter, and a fine filter, is considered. A numerical simulation for the prediction of the flow resistivity and filtering efficiency during a multi-pass test is performed. Some of the required model parameters are obtained from microscale simulations, i.e., the proposed method uses a multiscale approach. It is shown that the small and medium-sized particles are first mainly deposited right behind the interface, whereas after the growth of the cake, they rarely can pass the internal cake and are deposited right in front of the interface. In the beginning, the pressure drop is dominated by the second layer since the permeability of this layer is lower. It needs some time until the internal cake is the prevailing reason for the huge increase of the pressure drop.